AREA AND PERIMETER OF SECTORS

This item is taken from Cambridge International AS and A Level Mathematics (9709) Pure Mathematics 1 Paper 11 of May/June 2013.


To deal with this item, let us summarize the details of the problem:
   (a) Syllabus area: Circular Measure
   (b) Specific topic: Area of a Sector, Arc length
   (c) Formula needed:  

Let us determine first all the given in the figure.

To answer (i), we need to find the areas of the sectors in the figure. Our goal is to use the given relation between the areas of the two sectors to find the value of alpha.

To answer (ii), let us find the length of each side enclosing the given figure.

The perimeter of the figure is 

Therefore, 

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